Teachers, Learners and Oracles

TL;DR

This paper compares the efficiency of learning computably enumerable sets with teachers versus membership oracles, revealing significant resource differences under polynomial and exponential bounds.

Contribution

It introduces a family of sets that are learnable with teachers in polynomial time but require exponential resources with membership oracles, highlighting fundamental distinctions in learning models.

Findings

Sets learnable with teachers in polynomial time

Sets requiring exponential resources with membership oracles

Comparison across four measures of efficient learning

Abstract

We exhibit a family of computably enumerable sets which can be learned within polynomial resource bounds given access only to a teacher, but which requires exponential resources to be learned given access only to a membership oracle. In general, we compare the families that can be learned with and without teachers and oracles for four measures of efficient learning.